Thermal transport in phononic crystals: The role of zone folding effect

Recent experiments [Yu et al., Nature Nanotech 5, 718 (2010); Tang et al., Nano Lett. 10, 4279 (2010); Hopkins etal., Nano Lett. 11, 107(2011)] on silicon based nanoscale phononic crystals demonstrated substantially reduced thermal conductivity compared to bulk Si, which cannot be explained by incoherent phonon boundary scattering within the Boltzmann Transport Equation (BTE). In this paper, partial coherent treatment of phonons, where phonons are regarded as either wave or particles depending on their frequencies, was considered. Phonons with mean free path smaller than the characteristic size of phononic crystals are treated as particles and the transport in this regime is modeled by BTE with phonon boundary scattering taken into account. On the other hand, phonons with mean free path longer than the characteristic size are treated as waves. In this regime, phonon dispersion relations are computed using the Finite Difference Time Domain (FDTD) method and are found to be modified due to the zone folding ...